How many cups is in a bag that holds 31 servings, where a serving is 1.25 cups?

Question

How many cups is inside a bag that holds 31 servings? A serving size is considered one and a quarter cups.

Answer 1

Hi Sarah,

 

Your problem is a simple ratio and proportion problem.

You are given a ratio (rate to be more specific) of 1.25 cups per 1 serving. Using that ratio, you can set-up a proportion to find how many cups are there in 31 servings.

 

let x = number of cups per 31 servings

 

 1.25 cups   =        x cups

-------------         --------------

 1 serving            31 servings

 

 

    1.25  =     x   

    ------     -------     solve for x, cross multiply

      1           31

 

      x  =   38.75 cups

 

Be careful when you set-up your proportion, make sure the units of the numerators and denominators of the ratios are consistent.  If you used cups per serving on one  side, make sure the other side has the same set up of units.

 

Hope it helps.

 

Answer 2

To convert units without changing the value, we use the Multiplicative Identity (that is, 1).  Any number multiplied by 1 remains the same.  This process is called Dimensional Analysis.

 

For this problem:

  1 = ( ( 1 bag) / ( 31 servings ) ) = ( (31 servings ) / ( 1 bag ) )      [choose one]

  1 = ( ( 1 serving ) / ( 1.25 cups ) ) = ( ( 1.25 cups ) / ( 1 serving ) )     [choose one]

  [note: choose the one that cancels out the units]

 

1 bag

(1 bag)*1

(1 bag)*((31 servings)/(1 bag))*((1.25 cups)/(1 serving))    [bags & servings cancel, leaving only cups]

(1)*(31/1)*(1.25/1)  cups

  38.75 cups     [that is, 38 3/4]